Simplify the following expression: $t = \dfrac{-50a^3 - 10a^2}{-100a^3 - 50a^2}$ You can assume $a \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-50a^3 - 10a^2 = - (2\cdot5\cdot5 \cdot a \cdot a \cdot a) - (2\cdot5 \cdot a \cdot a)$ The denominator can be factored: $-100a^3 - 50a^2 = - (2\cdot2\cdot5\cdot5 \cdot a \cdot a \cdot a) - (2\cdot5\cdot5 \cdot a \cdot a)$ The greatest common factor of all the terms is $10a^2$ Factoring out $10a^2$ gives us: $t = \dfrac{(10a^2)(-5a - 1)}{(10a^2)(-10a - 5)}$ Dividing both the numerator and denominator by $10a^2$ gives: $t = \dfrac{-5a - 1}{-10a - 5}$